1. Field of the Invention
The present invention relates in general to the photonics field and, in particular, to a lens array and a method for fabricating the lens array that is relatively flat and has useful lenses with relatively uniform sag heights.
2. Description of Related Art
In the photonics field, one of the most significant design challenges involves the development of a new lens array which can be coupled to a fiber array to form a “near” ideal collimator array. Even though it is theoretically impossible to make a truly ideal collimator array, one can come very close if they can ensure that certain optical properties of a lens array are consistent for each of the lens in the lens array. To help ensure the consistency of these optical properties, one can make a lens array in accordance with the present invention that is relatively flat and has useful lenses with relatively uniform sag heights.
Referring to FIG. 1, there is illustrated a cross-sectional side view of an ideal collimator array 100 which includes an ideal fiber array 110 that is optically coupled to an ideal lens array 120 (shown in this example as a 1×8 lens array). The collimator array 100 has a series of collimators 100a-100h each of which includes an optical fiber 110a-110h and a lens 120a-120h that are optically coupled to one another. The function of a collimator 100a (for example) is to generate parallel rays of light 130a having a desired spot size by using the lens 120a to broaden a ray of light 140a exiting the optical fiber 110a. To obtain the desired spot size of the parallel rays of light 130a-130h for each of the collimators 100a-100h, several parameters need to be constant in each collimator 100a-100h. These parameter's include: (1) the distance (“d”) between each optical fiber 110a-110h and each lens 120a-120h; (2) the distance to beam waste (“DBW”); and (3) the mode field diameter (“MFD”). The ideal collimator array 100 in FIG. 1 shows these parameters and the equations below defines these parameters as follows:
 d=Lenses surface to fiber distance.  (1)
DBW=Distance to beam waste                     DBW        =                              f            ⁢                          {                                                                    z                    0                    2                                    ⁡                                      (                                          1                      -                                                                        ψ                          1                                                ⁢                                                  t                          ′                                                                                      )                                                  +                                                      [                                                                  t                        ′                                            +                                              d                        ⁡                                                  (                                                      1                            -                                                                                          ψ                                1                                                            ⁢                                                              t                                ′                                                                                                              )                                                                                      ]                                    ⁡                                      [                                                                  f                        ⁡                                                  (                                                      1                            -                                                                                          ψ                                2                                                            ⁢                                                              t                                ′                                                                                                              )                                                                    -                      d                                        ]                                                              }                                            {                                          z                0                2                            +                                                [                                                            f                      ⁡                                              (                                                  1                          -                                                                                    ψ                              2                                                        ⁢                                                          t                              ′                                                                                                      )                                                              -                    d                                    ]                                2                                      }                                              (        2        )            
where:
                t=plate thickness.        s1=back-side sag height.        s2=front-side sag height.        D=Lenses diameter.       c    i    =                    2        ⁢                  s          i                                                  (                          D              /              2                        )                    2                +                  s          i          2                      ⁢                   ⁢          curvature  of  lenses  surface.      curvature of lenses surface.        nl=Index of refraction of lenses material.        ω0=fiber mode diameter.       z    0    =            π      λ        ⁢          ω      0      2        ⁢                   ⁢          Rayleigh  range.      Rayleigh range.        λ=wavelength of light.        
φi=ciΔn=ci(nl−1)                     1        f            =                        ϕ          1                +                  ϕ          2                -                              ϕ            1                    ⁢                      ϕ            2                    ⁢                      t            ′                                ⁢                       f    =                            thick  lenses  focal  length,                ⁢                                   ⁢                  t          ′                    =              t        /                  n          l                    
f=thick lenses focal length, t′=t/nl 
                ψi=1−φit′MFD=Mode field diameter                     MFD        =                  ω          =                                                    (                                  λ                  π                                )                            ⁢                                                                                                                  (                                                                              f                            ⁢                                                                                                                   ⁢                                                          ψ                              1                                                                                -                          DBW                                                )                                            2                                        ⁢                                          z                      0                      2                                                        +                                                            [                                                                        f                          ⁢                                                                                                           ⁢                                                      t                            ′                                                                          +                                                  f                          ⁡                                                      (                                                                                          d                                ⁢                                                                                                                                   ⁢                                                                  ψ                                  1                                                                                            +                                                              DBW                                ⁢                                                                                                                                   ⁢                                                                  ψ                                  2                                                                                                                      )                                                                          -                                                  d                          ⁢                                                                                                           ⁢                          DBW                                                                    ]                                        2                                                                                        z                    0                                    ⁢                                      f                    ⁡                                          (                                                                        t                          ′                                                +                                                  f                          ⁢                                                                                                           ⁢                                                      ψ                            1                                                    ⁢                                                                                                           ⁢                                                      ψ                            2                                                                                              )                                                                                                                              (        3        )            * These equations are based on a lens array that has bi-convex lenses. However, it should be understood that the lens array of the present invention can have bi-convex lenses, plano-convex lenses or equi-convex lenses.        
Referring to these equations and the ideal collimator array 100 shown in FIG. 1, one can see that each lens 120a-120h in the lens array 120 must have the same configuration in order to have consistent parameters “d”, “DBW” and “MFD”. This assumes the fiber array 110 and lens array 120 are aligned to one another and that the fiber array 100 is able to hold the fibers 120a-120h a constant “d” away from each lens 120a-120h. 
Unfortunately, the traditional collimator 200 that has a lens array 220 produced from a photosensitive glass plate suffers from several problems which make it far from being an “ideal” lens array 120. Today it is well known that a lens array can be made from a photosensitive glass plate. In fact, scientists at Corning Incorporated the assignee of the present invention have developed and patented a photosensitive glass plate known as FOTOFORM® glass and a process known as the SMILE® process which can be used to form a lens array. The SMILE® process subjects the FOTOFORM® glass to an ultraviolet light exposure step, a heat treatment step and an ion exchange step in order to turn the FOTOFORM® glass into the lens array. A detailed discussion about the SMILE® process is provided in U.S. Pat. Nos. 4,572,611, 4,518,222 and 5,062,877 the contents of which are incorporated herein by reference. And, a detailed discussion about the FOTOFORM® glass is provided in U.S. Pat. Nos. 2,326,012, 2,422,472, 2,515,936, 2,515,938, 2,515,275, 2,515,942 and 2,515,943 the contents of which are incorporated herein by reference. An example of a traditional collimator array 200 that includes a lens array 220 that was fabricated from FOTOFORM® glass which was subjected to the SMILE® process is described below with respect to FIGS. 2A and 2B.
Referring to FIGS. 2A-2B, there are respectively illustrated a cross-sectional side view of the traditional collimator array 200 and a top view of the traditional lens array 220 (shown in this example as a 3×8 lens array). Like the ideal collimator array 100, the traditional array 200 includes a fiber array 210 holding optical fibers 220a-220h (only eight shown) that are optically coupled to the lenses 220a-220h in the lens array 220. The lenses 220a-220h are not close to having the same configurations and constant parameters “d”, “DBW” and “MFD” that are needed to form an ideal lens array 110. The traditional lens array 220 suffers from several problems including:                Non-uniform sag heights s1 and s2*.        A warped lens array 220**.        For large N×M lens arrays where N and M>>1, non-uniform shrinkage across the lens array can result in non-uniform pith values (pitch=distance between two lens center points).        
* Note that the outer lenses 220a and 220h have sag heights s1 and s2 that are higher than the sag heights s1 and s2 of the inner lenses 220b-220g. 
** An explanation as to why the traditional lens array 220 is warped is described below with respect to the lens array of the present invention. 
As can be seen, the traditional lens array 220 does not look like the ideal lens array 120 and as such the traditional lens array 220 does not function like the ideal lens array 120. This is because, all of the lenses 220a-220h are not uniform and do not have consistent optical parameters “d”, “DBW” and “MFD” like the lenses 120a-120h in the ideal lens array 120. And, since the lens array 220 is warped, the “d” dimensions are not the same between the optical fibers 210a-210h and the lenses 220a-220h. Accordingly, there is and has been a need for a lens array that does not suffer from the aforementioned shortcomings and other shortcomings of the traditional lens array. These needs and other needs are satisfied by the lens array and method of the present invention.